Question: In $2016$, the city of Rio de Janeiro had a population density of $5377\,\dfrac{\text{people}}{\text{km}^2}$. What was the population density of Rio de Janeiro in people per square meter?
Solution: We will convert $5377$ people per square kilometer to a rate in people per square meter using the following conversion rate: There are $1000\text{ m}$ per $1\text{ km}$. Therefore, there are $(1000\text{ m})^2=1{,}000{,}000\text{ m}^2$ in $1\text{ km}^2$. $\begin{aligned} &\phantom{=}\dfrac{5377\text{ people}}{1\text{ km}^2}\cdot\dfrac{1\text{ km}^2}{1{,}000{,}000\text{ m}^2} \\\\ &=\dfrac{5377\cdot1\cdot \text{people}\cdot \cancel{\text{km}^2}}{1\cdot1{,}000{,}000\cdot\cancel{\text{km}^2}\cdot\text{m}^2 } \\\\ &=\dfrac{5377}{1{,}000{,}000}\,\dfrac{\text{people}}{\text{m}^2} \\\\ &=0.005377 \,\dfrac{\text{people}}{\text{m}^2} \end{aligned}$ In conclusion, Rio de Janeiro's population density in people per square meter is: $0.005377 \,\dfrac{\text{people}}{\text{m}^2}$